Hamiltonian form of extended cubic-quintic nonlinear Schr\"odinger equation in a nonlinear Klein-Gordon model
Abstract
We derive an extended cubic-quintic nonlinear Schr\"odinger equation with Hamiltonian structure in a nonlinear Klein-Gordon model with cubic-quintic nonlinearity. We use the nonlinear dispersion relation to properly take into account the input of high-order nonlinear effects in the Hamiltonian perturbation approach to nonlinear modulation. We demonstrate that changing the balance between the cubic and quintic nonlinearities has a significant effect on the stability of unmodulated wave packets to long-wave modulations.
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